Prepare a medium-hot fire in a charcoal grill with a cover, or preheat a gas grill to medium-high. To make the topping, combine the chopped fresh basil and the mayonnaise in a shallow bowl. Cover and refrigerate until serving. To make the patties, heat the olive oil in a small fire-proof skillet on the grill rack. Add the onion, garlic cloves, parsley, oregano and mushroom and sauté until soft, about 5 minutes. Remove from the heat and set aside. Combine the ground chuck, chorico, egg, Italian seasoned bread crumbs, Red Wine, Sea Salt, pepper, hot sauce, mozzarella cheese and cheddar cheese in a large bowl. Add the sautéed items to the meat mixture and blend well. Divide the mixture into 6 equal portions and form into patties to fit into whole wheat pita pockets. When the grill is ready, brush the rack with vegetable oil. Place the patties on the rack, cover, and cook, turning once, just until done to preference, 3 to 5 minutes on each side for medium. To assemble the burgers, slice off and discard about one-fourth of each pita pocket and carefully spread the bread apart to form a pocket. Stuff a patty into each pocket and spoon an equal portion of the basil topping over each patty. Add a tomato slice and arrugla in each pocket and serve.